Seiberg-Witten Like equations on 5-dimensional contact metric manifolds

TL;DR

This paper formulates Seiberg-Witten-like equations on 5-dimensional contact metric manifolds, utilizing the Tanaka-Webster connection, and provides global solutions on strictly pseudoconvex CR manifolds, extending gauge theory concepts to odd dimensions.

Contribution

It introduces Seiberg-Witten equations on 5D contact metric manifolds using generalized Tanaka-Webster connections and establishes global solutions on certain CR manifolds, a novel extension of gauge theory.

Findings

Formulation of Seiberg-Witten equations on 5D contact manifolds

Use of Tanaka-Webster connection for Dirac operators

Existence of global solutions on strictly pseudoconvex CR manifolds

Abstract

In this paper, we write down Seiberg-Witten equations on contact metric manifolds of dimension 5. Any contact metric manifold has a spin^c structure. For Dirac equation we use Dirac type operators associated to the generalized Tanaka-Webster connection on spin^c spinor bundle of a contact metric manifold. For curvature equation we need to self-duality concept. Self-duality concept is significant on odd dimensional manifolds, particularly, on 5-dimensional contact manifolds. Finally, we give a global solution to these equations on strictly pseudoconvex CR manifolds.